Nonequilibrium Phase Transitions. Appendix A-F

摘要

A novel approach to a nonlinear nonequilibrium thermodynamics has been developed which predicts that the morphological structure and consequently the physical properties of polymeric materials might be controlled by dynamically fluctuating the external thermodynamic and/or pseudo-thermodynamic variables; measuring the response of the system to such fluctuations; and using this information to control the time evolution of the thermodynamic system. The theoretical development suggests replacing the concept of entropy with the concept of an excess energy. The excess energy of a nonequilibrium system-defined mathematically as the total Legendre transform of energy with respect to an independent set of extensive properties-plays the same role in nonequilibrium thermodynamics as do the free energy functions (i.e., partial Legendre transforms) in equilibrium thermodynamics. The partial Legendre transforms are functions of the (average) thermodynamic parameters whereas the total Legendre transform or excess energy is a functional or integral over both time and space of the gradients and the time rate of change of the thermodynamic and pseudo-thermodynamic parameters. At equilibrium there is no significant fluctuation about the average value of a thermodynamic parameter in either time or space so that the excess energy vanishes. (JHD)